How much power could a turbocharger generate?

That actually exists. It's called turbocompounding (https://www.dieselnet.com/tech/engine_whr_turbocompound.php). Sometimes the turbine is coupled directly to the crankshaft and there's no compressor. Sometimes there's no turbine (http://mechstuff.com/differences-between-superchargers-vs-turbochargers/).

Here's the power a turbine can produce:

dW/dt [W] = eff*dm/dt * c_p_mean * T_inlet*[(p_outlet/p_inlet)^((k-1)/k)-1]

T_inlet: Inlet temperature [K]. Usually 400-500 ºC for Otto engines and a around 600 ºC for Diesel engines. Let's take 873 K.

c_p_mean: Mean heat capacity at constant pressure [J/kgk]. Mean between T_inlet and T_outlet. For air it would probably be around 1050 J/kgK, but consult tables.

eff: Efficiency of the turbine. 0.80 is a typical value.

p_outlet: Outlet pressure [Pa]. Normally atmospheric pressure (101,325 Pa).

p_inlet: Inlet pressure [Pa]. Let's assume 200,000 Pa (2 bar), because the expansion isn't full.

k: Adiabatic index, usually 1.4 for air and similar for exhaust gases.

m: Mass [kg]. Its temporal derivative is mass flow [kg/s]. The same mass that enters must exit (ignoring leaks through the gaps). Let's say 4*10^-3 kg (I can't remember the figures I knew now). And 4 kg/s as the exhaust process takes place at a few miliseconds.

W: Work [J]. Its temporal derivate is power [W].

dW/dt = -514,458 W = -514.458 kW, which is too high. It could be from 1 to 10 kW, for example, depending chiefly on the mass flow and the expansion ratio (p_outlet/p_inlet).

Sorry for the terrible format, but I'm new to this forum and I don't know how to format yet. If you are going to convert the power to electrical power, multiply to 0.90 (usual efficiency of a electric generator/motor).

... could it be more effective to use this power to drive the wheels, rather than use it to spin a compresser as with a conventional turbocharger system?

No. The purpose of the e-machine on a turbocarger system is to make up any differences between the instantaneous torque demand of the compressor and the instananeous torque produced by the turbine. In order to have acceptable driveability and maximize performance, most turbochargers have a waste gate to manage torque mismatches which are designed to err on the side of excess turbine torque. With an e-motor adding or removing torque as needed, the turbocharger can be completely redesigned for better efficiency using simpler mechanicals and providing a wider operating envelope.

So the e-motor is there to service the turbocharger's need, not the other way around. You can build in a bias if you want, so that there is a net generator output, but this is extremely time variable, so all you can due is dump it into a battery storage system where it can be consumed as needed. This arrangement can't compete with the efficiency of crankshaft/tranny/shafting/wheels. A crankshaft generator would be a better way to generate electrical traction power.

Currently, the biggest problem with producing these systems is cooling them. Electrical motors don't like the sort of temps found next to the turbo. I expect the first couple generations of these that we will see will not be doing much extra generator-wise. That only adds to the heat problem.